Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Nonlinear Incremental Approach for Replay Attack Detection

Tao Chen, Andreu Cecilia, Lei Wang, Daniele Astolfi, Zhitao Liu

Abstract

Replay attacks comprise replaying previously recorded sensor measurements and injecting malicious signals into a physical plant, causing great damage to cyber-physical systems. Replay attack detection has been widely studied for linear systems, whereas limited research has been reported for nonlinear cases. In this paper, the replay attack is studied in the context of a nonlinear plant controlled by an observer-based output feedback controller. We first analyze replay attack detection using an innovation-based detector and reveal that this detector alone may fail to detect such attacks. Consequently, we turn to a watermark-based design framework to improve the detection. In the proposed framework, the effects of the watermark on attack detection and closed-loop system performance loss are quantified by two indices, which exploit the incremental gains of nonlinear systems. To balance the detection performance and control system performance loss, an explicit optimization problem is formulated. Moreover, to achieve a better balance, we generalize the proposed watermark design framework to co-design the watermark, controller and observer. Numerical simulations are presented to validate the proposed frameworks.

A Nonlinear Incremental Approach for Replay Attack Detection

Abstract

Replay attacks comprise replaying previously recorded sensor measurements and injecting malicious signals into a physical plant, causing great damage to cyber-physical systems. Replay attack detection has been widely studied for linear systems, whereas limited research has been reported for nonlinear cases. In this paper, the replay attack is studied in the context of a nonlinear plant controlled by an observer-based output feedback controller. We first analyze replay attack detection using an innovation-based detector and reveal that this detector alone may fail to detect such attacks. Consequently, we turn to a watermark-based design framework to improve the detection. In the proposed framework, the effects of the watermark on attack detection and closed-loop system performance loss are quantified by two indices, which exploit the incremental gains of nonlinear systems. To balance the detection performance and control system performance loss, an explicit optimization problem is formulated. Moreover, to achieve a better balance, we generalize the proposed watermark design framework to co-design the watermark, controller and observer. Numerical simulations are presented to validate the proposed frameworks.

Paper Structure

This paper contains 29 sections, 15 theorems, 97 equations, 8 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries on incremental gain properties
  3. Problem Formulation
  4. System Description
  5. Communication Topology and Replay Attack
  6. Innovation-based Replay Attack Detection
  7. Watermark-based Replay Attack Detection
  8. Replay Attack Detection Performance
  9. Control System Performance Loss
  10. Two Examples of Watermark Signal $\xi(t)$
  11. Chaotic Watermark
  12. Bernoulli Watermark
  13. Design of the Watermark Gain
  14. Sufficient Conditions for Incremental Gains
  15. An Algorithm for Watermark Gain Design
  16. ...and 14 more sections

Key Result

Proposition 1

Suppose there exist a $\mathcal{C}^1$ function $V^+:{\mathbb R}^n\times {\mathbb R}^n\times{\mathbb R}\to {\mathbb R}_{\geq0}$ , functions $\underline\alpha^+, \mkern 1.5mu\overline{\mkern-1.5mu\alpha\mkern-1.5mu}\mkern 1.5mu^+\in \mathcal{K}_\infty$ and $\gamma^+>0$ such that for all $t\geq0$, $x_1,x_2\in {\mathbb R}^n$, and $u_1,u_2\in \mathcal{U}$. Then the $\mathcal{L}^+_{\delta 2}$ gain of s

Figures (8)

  • Figure 1: Scheme of the communication topology.
  • Figure 2: Scheme of the communication topology and security layer.
  • Figure 3: The $\beta_i$ solved by iterative LMI.
  • Figure 4: The detection performance with chaotic watermark.
  • Figure 5: The states of the plant with chaotic watermark. (a) With $K_0, L_0$ and $G_0$. (b) With $K_\text{opt}, L_\text{opt}$ and $G_\text{opt}$.
  • ...and 3 more figures

Theorems & Definitions (34)

  • Definition 1: ISS
  • Definition 2: $\delta$ISS
  • Definition 3: $\mathcal{L}^+_{\delta 2}$ gain
  • Definition 4: $\mathcal{L}^-_{\delta 2}$ gain
  • Remark 1
  • Remark 2
  • Proposition 1: Lyapunov $\mathcal{L}^+_{\delta 2}$ characterization
  • Proposition 2: Lyapunov $\mathcal{L}^-_{\delta 2}$ characterization
  • Lemma 1
  • Lemma 2
  • ...and 24 more